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Question: 5 20 consider a contest where two contestants i e...

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5. [20] Consider a contest where two contestants, i E (1,2), compete for a prize worth v (in utility terms). The probability of contestant i wining the compe- P(a, ea) = el + e2, where e is the effort exerted by contestant i. The losing contestant gets nothing. The (utility) cost of effort is cfe) et. Thus, contestant is payoff tition is is given by (a) [8] Find the symmetric Nash equilibrium effort level. (b) 14] Given an interpretation of r. Give an interpretation of what happens to the equilibrium effort level as r-0 (e) 8l Now, suppose r 2 and the contestants are restricted to putting in one of two effort levels: high (e 3) or low (e4 1). Find all the Nash equilibria (including mixed strategy ones).
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